# Nonlinear dynamics of Josephson vortices in merging superfluid rings

## TL;DR

This paper investigates the complex nonlinear dynamics of Josephson vortices during the merging of two superfluid rings with different vorticities, revealing 3D vortex evolution, instabilities, and the influence of initial conditions.

## Contribution

It provides new insights into 3D vortex behavior and the effects of initial population imbalance and trap shape on superfluid ring mergers.

## Key findings

- Josephson vortices emerge in the barrier during ring merging.
- Kelvin-Helmholtz instability can develop at the interface.
- Final vortex states depend on initial conditions and trap geometry.

## Abstract

We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between the superflows. When the barrier is gradually eliminated, we observe essentially three-dimensional evolution of quantum vortices, which may include the development of the Kelvin-Helmholtz instability at the interface between the rings, in the framework of a weakly dissipative Gross-Pitaevskii equation. An initially more populated ring, carrying a persistent current, can drag an initially non-rotating less populated one into the same vortex state. The final state of the condensate crucially depends on an initial population imbalance in the double-ring set, as well as on the shape of the 3D trapping potential, oblate or prolate. In the prolate (axially elongated) configuration, robust 3D hybrid structures may appear as a result of the merger of persistent currents corresponding to different vorticities.